Improper Integral (Type 2)

Even if f(x) has an infinite dicsontinuity at 0, we can sometimes make sense of the integral of f(x) from 0 to 1, but taking a limit of the integral of f(x) from t to 1 as t goes to 0. Below we measure this integral for various values of t and try to decide whether the integral of f(x)dx from 0 to 1 is finite or not.
(f(x) = 1/x² initially.)

-Drag the slider to change the value of t.
- Type "f(x) = ___" to change the function.

Jason McCullough, Created with GeoGebra